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6. 2D Kinematic Equations You are planning a demonstration where a "basketball" made of hardwood, and painted orange, will be fired over a 3.00m high wall and go through the basketball net to "make a basket". The "ball" is fired along the cannon barrel at 20m/s. Both the mouth of the cannon and the basket are 1.00m above the flat ground. The wall is 9.00 m from the cannon, and the net is 9.00m from the wall; all along a straight line. 9.00m 9.00m 1.00m 6.1 What cannon angle(s), in degrees, will make a basket without hitting the wall? Hint#1 is time to range 2 (time to peak) Hint#2 is a trig theorem: 2sin@cose = sin(20) Hint#3: Let o = (20), then note that the equation Sin(o)=n where 0sns1, has two solutions on the unit circle: 202 20, 20 sin(20)

6. 2D Kinematic Equations You are planning a demonstration where a "basketball" made of hardwood, and painted orange, will be fired over a 3.00m high wall and go through the basketball net to "make a basket". The "ball" is fired along the cannon barrel at 20m/s. Both the mouth of the cannon and the basket are 1.00m above the flat ground. The wall is 9.00 m from the cannon, and the net is 9.00m from the wall; all along a straight line. 9.00m 9.00m 1.00m 6.1 What cannon angle(s), in degrees, will make a basket without hitting the wall? Hint#1 is time to range 2 (time to peak) Hint#2 is a trig theorem: 2sin@cose = sin(20) Hint#3: Let o = (20), then note that the equation Sin(o)=n where 0sns1, has two solutions on the unit circle: 202 20, 20 sin(20)

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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### 6. 2D Kinematic Equations You are planning a demonstration where a "basketball" made of hardwood and painted orange will be fired over a 3.00 m high wall and go through the basketball net to "make a basket." The "ball" is fired along the cannon barrel at 20 m/s. Both the mouth of the cannon and the basket are 1.00 m above the flat ground. The wall is 9.00 m from the cannon, and the net is 9.00 m from the wall; all are aligned along a straight line. #### 6.1 What cannon angle(s), in degrees, will make a basket without hitting the wall? - **Hint #1**: Time to range = 2 × (time to peak) - **Hint #2**: A trig theorem: \(2 \sin \theta \cos \theta = \sin(2\theta)\) - **Hint #3**: Let \(\Phi = (2\theta)\), then note that the equation \(\sin(\Phi) = n\) where \(0 \leq n \leq 1\), has two solutions on the unit circle. #### Diagram Explanation The diagram includes a cannon firing a ball over a wall toward a basketball net. The wall is 3.00 m high. The cannon and the net are both at a height of 1.00 m off the ground. The distances between the cannon, the wall, and the net are marked as 9.00 m. Below the scenario illustration is a unit circle diagram that visually represents the angles \(2\theta_1\) and \(2\theta_2\) as possible solutions for the cannon angle. The relationship between angle \(2\theta\) and the sine function on the unit circle is depicted.
Transcribed Image Text:### 6. 2D Kinematic Equations You are planning a demonstration where a "basketball" made of hardwood and painted orange will be fired over a 3.00 m high wall and go through the basketball net to "make a basket." The "ball" is fired along the cannon barrel at 20 m/s. Both the mouth of the cannon and the basket are 1.00 m above the flat ground. The wall is 9.00 m from the cannon, and the net is 9.00 m from the wall; all are aligned along a straight line. #### 6.1 What cannon angle(s), in degrees, will make a basket without hitting the wall? - **Hint #1**: Time to range = 2 × (time to peak) - **Hint #2**: A trig theorem: \(2 \sin \theta \cos \theta = \sin(2\theta)\) - **Hint #3**: Let \(\Phi = (2\theta)\), then note that the equation \(\sin(\Phi) = n\) where \(0 \leq n \leq 1\), has two solutions on the unit circle. #### Diagram Explanation The diagram includes a cannon firing a ball over a wall toward a basketball net. The wall is 3.00 m high. The cannon and the net are both at a height of 1.00 m off the ground. The distances between the cannon, the wall, and the net are marked as 9.00 m. Below the scenario illustration is a unit circle diagram that visually represents the angles \(2\theta_1\) and \(2\theta_2\) as possible solutions for the cannon angle. The relationship between angle \(2\theta\) and the sine function on the unit circle is depicted.
Expert Solution
Step 1

Given:

horizontal range R = 18 m

u =20 m/s

H= 3.0 m

 

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